Problem: Solve for $x$ and $y$ using elimination. ${4x+y = 20}$ ${-5x-y = -23}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {4x+y = 20}\thinspace$ to find $y$ ${4}{(3)}{ + y = 20}$ $12+y = 20$ $12{-12} + y = 20{-12}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-5x-y = -23}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ - y = -23}$ ${y = 8}$